All factors of a number, factor pairs and prime factorisation — with division steps.
Enter a whole number. The factor calculator lists every factor, pairs them up, and breaks the number into its prime factorisation with the steps shown.
All factors
How to use this tool
Type a whole number into the factor calculator — 36 is the default example. Decimals and fractions are not accepted, because factors are defined for whole numbers.
Every factor is listed in order, from 1 up to the number itself, with the total count. If the list looks short, your number may be prime.
Factors are paired (1 × 36, 2 × 18, …) and the prime factorisation is shown with each division step, so the working is visible rather than just the answer.
Copy the full factor list and prime factorisation for homework or a worksheet.
Formula & worked example
Worked example: the factor calculator for 36 gives 1, 2, 3, 4, 6, 9, 12, 18, 36 — 9 factors in total. Paired up they are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6, and they add up to 91. The prime factorisation, dividing out the smallest prime at each step (36 ÷ 2 = 18, 18 ÷ 2 = 9, 9 ÷ 3 = 3), is 36 = 2² × 3². The proper divisors add to 55, less than 36, so 36 is a deficient number — and because 6 × 6 = 36, it is also a perfect square.
Limitations — read this before you rely on it
Factors are defined for positive whole numbers, so this calculator rejects 0, negatives, decimals and fractions. The number 1 is a special case: it has a single factor and is neither prime nor composite. Numbers above 100,000,000,000 are rejected because listing factors by trial division gets slow; for such numbers, use the prime-factorisation route of the GCF or scientific tools instead.
Frequently asked questions
A factor of a number is a whole number that divides it exactly, with no remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Every number has 1 and itself as factors; the interesting ones are in between.
Test each whole number up to the square root of your number: if it divides exactly, both it and its partner (the quotient) are factors. That is why this calculator only needs to test up to √36 = 6 for the number 36 — every factor above 6 is the partner of one below it.
Prime factorisation breaks a number into primes only: 36 = 2² × 3². Divide out the smallest prime factor repeatedly (36 ÷ 2 = 18, 18 ÷ 2 = 9, 9 ÷ 3 = 3) until only a prime remains. The steps above show this working for your number.
A prime number has exactly two factors, 1 and itself — 17, for example, has only 1 and 17. A composite number has more than two factors. 1 is neither: it has only one factor. This calculator labels your number for you.
They are different jobs. This factor calculator lists every factor of one number. The greatest common factor (GCF) is the largest factor shared by two or more numbers — use the GCF Calculator for that. But note: the GCF of two numbers must always be a factor of each of them, which is why the factor list is the starting point.